Acyclic domains of linear orders: a survey

Bernard Monjardet

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Abstract: Among the many significant contributions that Fishburn made to social choice theory some have focused on what he has called "acyclic sets", i.e. the sets of linear orders where majority rule applies without the "Condorcet effect" (majority relation never has cycles). The search for large domains of this type is a fascinating topic. I review the works in this field and in particular consider a recent one that allows to show the connections between some of them that have been unrelated up to now.

Keywords: acyclic set; alternating scheme; distributive lattice; effet Condorcet; linear order; maximal chain; permutoèdre lattice; single-peaked domain; weak Bruhat order; value restriction.; value restriction; chaîne maximale; domaine Condorcéen; ordre faible de Bruhat; ordre unimodal; ordre total; permutoèdre; treillis distributif (search for similar items in EconPapers)
Date: 2009-02
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00198635
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Citations: View citations in EconPapers (20)

Published in Steven Brams, William V. Gehrlein, Fred S. Roberts. The Mathematics of Preference, Choice and Order, Essays in honor of Peter C. Fishburn, Springer, pp.139-160, 2009, Studies in Choice and Welfare, ⟨10.1007/978-3-540-79128-7_8⟩

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Related works:
Chapter: Acyclic Domains of Linear Orders: A Survey (2009)
Working Paper: Acyclic domains of linear orders: a survey (2009)
Working Paper: Acyclic domains of linear orders: a survey (2007)
Working Paper: Acyclic domains of linear orders: a survey (2007)
Working Paper: Acyclic domains of linear orders: a survey (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00198635

DOI: 10.1007/978-3-540-79128-7_8

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